By: Ashley and Christine
Phy 200
Professor Newman
4/13/12
What is it?
 Technique used to settle particles in solution against the
barrier using centrifugal acceleration
Two Types of Centrifuges
Analytical
Non Analytical
History
 1913 - Dumansky proposed the use of ultracentrifugation to determine
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dimensions of particles
1923 - The first centrifuge is constructed by Svedberg and Nichols.
1929 - Lamm deduces a general equation that describes the movement
within the ultracentrifuge field
1940s - Spinco Model E centrifuge becomes commercially available
1950s - Sedimentation becomes a widely used method.
1960s - First scanning photoelectric absorption optical system developed
1980s - Sedimentation loses popularity due to data treatment being slow
and the creation of gel electrophoresis and chromatography
1990s - Newer versions of centrifuge gains popularity again
2000s - It is now recognized as a necessary technique for most laboratories
How Does It Work?
 Everything has a sedimentation coefficient
 Ratio of measured velocity of the particle to its centrifugal
acceleration
 Can be calculated from the forces acting on a particle in the
cell
Sedimentation Coefficient
 Usually, determine mass by observing movement of
particles due to known forced
 Use Gravity normally
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For molecules, force is too small
 Avoid this by increasing PE by putting paricles in a cell
rotating at a high speed
 Get Sedimentation Coefficient
How does it work?
 Rotors must be capable of withstanding large
gravitational stress
 Two types of cells: double sector (accounts for
absorbing components in solvent) and
boundary forming (allows for layering of
solvent over the solution)
 Optical detection systems: Rayleigh optical
system (displays boundaries in terms of
refractive index as a function of radius),
Schlieren optical system (refractive index
gradient as a function of radius), and
absorption optical system (optical density as a
function of radius)
 Data acquisition is computer automated due
to the Beckman Instruments Optima XL
analytical centrifuge
Deriving the Lamm Equation
 Describes the transport process in the ultracentrifuge
 Fick’s first equation:
 Jx = -D[dC/dx]
 If all particles in the cell drift in a +x direction at speed, u:
 Jx = -D[dC/dx] + uC(x)
 u = sω2x
 Therefore, Jx = -D[dC/dx] + sω2xC(x)
 For ideal infinite cell lacking walls.
Lamm Equation
 For real experimental conditions:
 Cross-section of a sector cell is proportional to r
 Continuity equation:
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(dC/dt)r= -(1/r)(drJ/dr)t
 Combine ideal equation with continuity equation to obtain:
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(dC/dt)r = -(1/r){(d/dr)[ω2r2sC – Dr(dc/dr)t]}t
 Describes diffusion with drift in an AUC sector cell under
real experimental conditions.
http://www.nibib.nih.gov/Research/Intramural/lbps/pbr/auc/LammEqSoluti
ons
Lamm Equation: Different
Boundary Conditions
 Exact Solutions Exist in 2 limiting cases:
 1. “NO DIFFUSION”
 Homogeneous macromolecular solution
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C2(x,t) = {0
if xm<x<xavg
{C0exp(-2sω2t)
if xavg<x<xb
 2. “NO SEDIMENTATION”
 Lamm Equation: (dC/dt)r = -D(d2C/dt2)t
 Concentration Gradient: (dC/dt)r = -Co(πDt)1/2exp(-x2/4Dt)
 Diffusion coefficient determined by measuring the standard
deviation of Gaussian curve
 Used for small globular proteins, at low speed, with synthetic
boundary cell.
Technology Enabling Analytical
Analysis
 Two computer modeling methods enable simultaneous
determination of sedimentation, diffusion coefficients, and
http://www.aapsj.org/view.asp?art=aa
molecular mass.
psj080368
 1. vanHolde-Weischet Method:
 Extrapolation to infinite time must eliminate the contribution
of diffusion to the boundary shape.
 ULTRASCAN software
 2.Stafford Method:
 Sedimentation coefficient distribution is computed from the
time derivate of the sedimentation velocity concentration
profile
http://www.ultrascan2.uthscsa.edu/tutorial/basics_5.html
Specific Boundary Conditions
 Faxen-type solutions:
 Centrifugation cell considered infinite sector
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Diffusion is small
Only consider early sedimentation times
 Archibald solutions:
 S and D considered constant
 Fujita-type solutions:
 D is constant
 S depends on concentration
VelocityEquilibrium
Sedimentation
Sedimentation Sedimentation
Velocity and
Equilibrium
Angular Velocity
Large
(according to
sedimentation
properties)
Small
Analysis
As a function of time
At equilibrium
Measurement
Forming a Boundary
Particle distribution in
cell
Calculated Parameters
Shape, mass composition Mass composition
Sedimentation Velocity
 How we measure the results: Determine the Sedimentation
and Diffusion Coefficients from a moving boundary
It takes a While to Run an
Experiment!
Speed (rpm)
Time at each speed (s) Svedbergs
0-6000
15
500
6000
600
4220
9000
600
1330
13000
600
550
18000
600
250
25000
600
125
50000
3600
31
Correcting to Standard Value
 Allows for standardization of sedimentation coefficients
Concentration Dependence
 Sedimentation coefficients of biological macromolecules
are normally obtained at finite concentration and should
be extrapolated to zero concentration
Determining Macromolecular Mass
 First Svedberg equation:
 M = sRT/D(1-υavgρo)
 Assumptions:
 Frictional coefficients affecting diffusion and sedimentation
are identical
Sedimentation Equilibrium
 Even if centrifuged for an extended period of time,
macromolecules will not join pellet because of
gravitational and diffusion force equilibrium.
 Molecular mass determination is independent of shape.
 Shape only affects rate equilibrium is reached, not
distribution.
 No changes in concentration with time at equilibrium
 Total flux = 0
Binding Constants
 Can measure concentration dependence of an effective
average molecular mass.
 Can be used to describe different kinds of phenomenon.
 Dissociation equilibrium constant can be directly
determined from the equilibrium sedimentation data
 C(r) = CA(r)σA + CB(r)σB + CAB(r)σAB
Partial Specific Volume
 Needed when determining molecular mass through
sedimentation
 Measurement of the density of the particle using its
calculated volume and mass
 Very difficult to make precise density measurements
needed
Density Gradient Sedimentation
 Velocity Zonal Method
 Layered density gradient
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Sucrose, glycerol
 Particles separate into zones based on sedimentation velocity,
according to sedimentation coefficients
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Determined by size, shape, and buoyant density
Estimation of molecular masses
Potential Problem:
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Molecular crowding effect due to high sucrose concentration
 Density Gradient Sedimentation Equilibrium
 Density gradient itself formed by centrifugal field
 Used in experiment by Messelson and Stahl
http://www.mun.ca/biology/scarr/Gr10-23.html
Molecular Shape
 Sedimentation coefficient
dependent on particle volume
and shape
 Molecules having the same
shape, but different molecular
mass form a homologous
series.
http://web.virginia.edu/Heidi/chapter30
/chp30.htm